2t^2-12t-12=0

Solution for 2t^2-12t-12=0 equation:

Simplifying
2t2 + -12t + -12 = 0

Reorder the terms:
-12 + -12t + 2t2 = 0

Solving
-12 + -12t + 2t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -6t + t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -6t + t2)' equal to zero and attempt to solve:

Simplifying
-6 + -6t + t2 = 0

Solving
-6 + -6t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -6t + 6 + t2 = 0 + 6

Reorder the terms:
-6 + 6 + -6t + t2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -6t + t2 = 0 + 6
-6t + t2 = 0 + 6

Combine like terms: 0 + 6 = 6
-6t + t2 = 6

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = 6 + 9

Reorder the terms:
9 + -6t + t2 = 6 + 9

Combine like terms: 6 + 9 = 15
9 + -6t + t2 = 15

Factor a perfect square on the left side:
(t + -3)(t + -3) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(t + -3) equal to 3.872983346 and -3.872983346.

Subproblem 1
t + -3 = 3.872983346

Simplifying
t + -3 = 3.872983346

Reorder the terms:
-3 + t = 3.872983346

Solving
-3 + t = 3.872983346

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + t = 3.872983346 + 3

Combine like terms: -3 + 3 = 0
0 + t = 3.872983346 + 3
t = 3.872983346 + 3

Combine like terms: 3.872983346 + 3 = 6.872983346
t = 6.872983346

Simplifying
t = 6.872983346

Subproblem 2
t + -3 = -3.872983346

Simplifying
t + -3 = -3.872983346

Reorder the terms:
-3 + t = -3.872983346

Solving
-3 + t = -3.872983346

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + t = -3.872983346 + 3

Combine like terms: -3 + 3 = 0
0 + t = -3.872983346 + 3
t = -3.872983346 + 3

Combine like terms: -3.872983346 + 3 = -0.872983346
t = -0.872983346

Simplifying
t = -0.872983346

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.872983346, -0.872983346}
Solution
t = {6.872983346, -0.872983346}